SelfadjointMatrixVector.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_SELFADJOINT_MATRIX_VECTOR_H
11 #define EIGEN_SELFADJOINT_MATRIX_VECTOR_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 /* Optimized selfadjoint matrix * vector product:
18  * This algorithm processes 2 columns at onces that allows to both reduce
19  * the number of load/stores of the result by a factor 2 and to reduce
20  * the instruction dependency.
21  */
22 
23 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version=Specialized>
25 
26 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
28 
29 {
30 static EIGEN_DONT_INLINE void run(
31  Index size,
32  const Scalar* lhs, Index lhsStride,
33  const Scalar* _rhs, Index rhsIncr,
34  Scalar* res,
35  Scalar alpha);
36 };
37 
38 template<typename Scalar, typename Index, int StorageOrder, int UpLo, bool ConjugateLhs, bool ConjugateRhs, int Version>
40  Index size,
41  const Scalar* lhs, Index lhsStride,
42  const Scalar* _rhs, Index rhsIncr,
43  Scalar* res,
44  Scalar alpha)
45 {
46  typedef typename packet_traits<Scalar>::type Packet;
47  const Index PacketSize = sizeof(Packet)/sizeof(Scalar);
48 
49  enum {
50  IsRowMajor = StorageOrder==RowMajor ? 1 : 0,
51  IsLower = UpLo == Lower ? 1 : 0,
52  FirstTriangular = IsRowMajor == IsLower
53  };
54 
55  conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> cj0;
56  conj_helper<Scalar,Scalar,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> cj1;
58 
59  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, IsRowMajor), ConjugateRhs> pcj0;
60  conj_helper<Packet,Packet,NumTraits<Scalar>::IsComplex && EIGEN_LOGICAL_XOR(ConjugateLhs, !IsRowMajor), ConjugateRhs> pcj1;
61 
62  Scalar cjAlpha = ConjugateRhs ? numext::conj(alpha) : alpha;
63 
64  // FIXME this copy is now handled outside product_selfadjoint_vector, so it could probably be removed.
65  // if the rhs is not sequentially stored in memory we copy it to a temporary buffer,
66  // this is because we need to extract packets
67  ei_declare_aligned_stack_constructed_variable(Scalar,rhs,size,rhsIncr==1 ? const_cast<Scalar*>(_rhs) : 0);
68  if (rhsIncr!=1)
69  {
70  const Scalar* it = _rhs;
71  for (Index i=0; i<size; ++i, it+=rhsIncr)
72  rhs[i] = *it;
73  }
74 
75  Index bound = (std::max)(Index(0),size-8) & 0xfffffffe;
76  if (FirstTriangular)
77  bound = size - bound;
78 
79  for (Index j=FirstTriangular ? bound : 0;
80  j<(FirstTriangular ? size : bound);j+=2)
81  {
82  register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
83  register const Scalar* EIGEN_RESTRICT A1 = lhs + (j+1)*lhsStride;
84 
85  Scalar t0 = cjAlpha * rhs[j];
86  Packet ptmp0 = pset1<Packet>(t0);
87  Scalar t1 = cjAlpha * rhs[j+1];
88  Packet ptmp1 = pset1<Packet>(t1);
89 
90  Scalar t2(0);
91  Packet ptmp2 = pset1<Packet>(t2);
92  Scalar t3(0);
93  Packet ptmp3 = pset1<Packet>(t3);
94 
95  size_t starti = FirstTriangular ? 0 : j+2;
96  size_t endi = FirstTriangular ? j : size;
97  size_t alignedStart = (starti) + internal::first_aligned(&res[starti], endi-starti);
98  size_t alignedEnd = alignedStart + ((endi-alignedStart)/(PacketSize))*(PacketSize);
99 
100  // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
101  res[j] += cjd.pmul(numext::real(A0[j]), t0);
102  res[j+1] += cjd.pmul(numext::real(A1[j+1]), t1);
103  if(FirstTriangular)
104  {
105  res[j] += cj0.pmul(A1[j], t1);
106  t3 += cj1.pmul(A1[j], rhs[j]);
107  }
108  else
109  {
110  res[j+1] += cj0.pmul(A0[j+1],t0);
111  t2 += cj1.pmul(A0[j+1], rhs[j+1]);
112  }
113 
114  for (size_t i=starti; i<alignedStart; ++i)
115  {
116  res[i] += t0 * A0[i] + t1 * A1[i];
117  t2 += numext::conj(A0[i]) * rhs[i];
118  t3 += numext::conj(A1[i]) * rhs[i];
119  }
120  // Yes this an optimization for gcc 4.3 and 4.4 (=> huge speed up)
121  // gcc 4.2 does this optimization automatically.
122  const Scalar* EIGEN_RESTRICT a0It = A0 + alignedStart;
123  const Scalar* EIGEN_RESTRICT a1It = A1 + alignedStart;
124  const Scalar* EIGEN_RESTRICT rhsIt = rhs + alignedStart;
125  Scalar* EIGEN_RESTRICT resIt = res + alignedStart;
126  for (size_t i=alignedStart; i<alignedEnd; i+=PacketSize)
127  {
128  Packet A0i = ploadu<Packet>(a0It); a0It += PacketSize;
129  Packet A1i = ploadu<Packet>(a1It); a1It += PacketSize;
130  Packet Bi = ploadu<Packet>(rhsIt); rhsIt += PacketSize; // FIXME should be aligned in most cases
131  Packet Xi = pload <Packet>(resIt);
132 
133  Xi = pcj0.pmadd(A0i,ptmp0, pcj0.pmadd(A1i,ptmp1,Xi));
134  ptmp2 = pcj1.pmadd(A0i, Bi, ptmp2);
135  ptmp3 = pcj1.pmadd(A1i, Bi, ptmp3);
136  pstore(resIt,Xi); resIt += PacketSize;
137  }
138  for (size_t i=alignedEnd; i<endi; i++)
139  {
140  res[i] += cj0.pmul(A0[i], t0) + cj0.pmul(A1[i],t1);
141  t2 += cj1.pmul(A0[i], rhs[i]);
142  t3 += cj1.pmul(A1[i], rhs[i]);
143  }
144 
145  res[j] += alpha * (t2 + predux(ptmp2));
146  res[j+1] += alpha * (t3 + predux(ptmp3));
147  }
148  for (Index j=FirstTriangular ? 0 : bound;j<(FirstTriangular ? bound : size);j++)
149  {
150  register const Scalar* EIGEN_RESTRICT A0 = lhs + j*lhsStride;
151 
152  Scalar t1 = cjAlpha * rhs[j];
153  Scalar t2(0);
154  // TODO make sure this product is a real * complex and that the rhs is properly conjugated if needed
155  res[j] += cjd.pmul(numext::real(A0[j]), t1);
156  for (Index i=FirstTriangular ? 0 : j+1; i<(FirstTriangular ? j : size); i++)
157  {
158  res[i] += cj0.pmul(A0[i], t1);
159  t2 += cj1.pmul(A0[i], rhs[i]);
160  }
161  res[j] += alpha * t2;
162  }
163 }
164 
165 } // end namespace internal
166 
167 /***************************************************************************
168 * Wrapper to product_selfadjoint_vector
169 ***************************************************************************/
170 
171 namespace internal {
172 template<typename Lhs, int LhsMode, typename Rhs>
173 struct traits<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true> >
174  : traits<ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs> >
175 {};
176 }
177 
178 template<typename Lhs, int LhsMode, typename Rhs>
179 struct SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>
180  : public ProductBase<SelfadjointProductMatrix<Lhs,LhsMode,false,Rhs,0,true>, Lhs, Rhs >
181 {
183 
184  enum {
185  LhsUpLo = LhsMode&(Upper|Lower)
186  };
187 
188  SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
189 
190  template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
191  {
192  typedef typename Dest::Scalar ResScalar;
193  typedef typename Base::RhsScalar RhsScalar;
194  typedef Map<Matrix<ResScalar,Dynamic,1>, Aligned> MappedDest;
195 
196  eigen_assert(dest.rows()==m_lhs.rows() && dest.cols()==m_rhs.cols());
197 
198  typename internal::add_const_on_value_type<ActualLhsType>::type lhs = LhsBlasTraits::extract(m_lhs);
199  typename internal::add_const_on_value_type<ActualRhsType>::type rhs = RhsBlasTraits::extract(m_rhs);
200 
201  Scalar actualAlpha = alpha * LhsBlasTraits::extractScalarFactor(m_lhs)
202  * RhsBlasTraits::extractScalarFactor(m_rhs);
203 
204  enum {
205  EvalToDest = (Dest::InnerStrideAtCompileTime==1),
206  UseRhs = (_ActualRhsType::InnerStrideAtCompileTime==1)
207  };
208 
211 
212  ei_declare_aligned_stack_constructed_variable(ResScalar,actualDestPtr,dest.size(),
213  EvalToDest ? dest.data() : static_dest.data());
214 
215  ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhsPtr,rhs.size(),
216  UseRhs ? const_cast<RhsScalar*>(rhs.data()) : static_rhs.data());
217 
218  if(!EvalToDest)
219  {
220  #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
221  int size = dest.size();
222  EIGEN_DENSE_STORAGE_CTOR_PLUGIN
223  #endif
224  MappedDest(actualDestPtr, dest.size()) = dest;
225  }
226 
227  if(!UseRhs)
228  {
229  #ifdef EIGEN_DENSE_STORAGE_CTOR_PLUGIN
230  int size = rhs.size();
231  EIGEN_DENSE_STORAGE_CTOR_PLUGIN
232  #endif
233  Map<typename _ActualRhsType::PlainObject>(actualRhsPtr, rhs.size()) = rhs;
234  }
235 
236 
237  internal::selfadjoint_matrix_vector_product<Scalar, Index, (internal::traits<_ActualLhsType>::Flags&RowMajorBit) ? RowMajor : ColMajor, int(LhsUpLo), bool(LhsBlasTraits::NeedToConjugate), bool(RhsBlasTraits::NeedToConjugate)>::run
238  (
239  lhs.rows(), // size
240  &lhs.coeffRef(0,0), lhs.outerStride(), // lhs info
241  actualRhsPtr, 1, // rhs info
242  actualDestPtr, // result info
243  actualAlpha // scale factor
244  );
245 
246  if(!EvalToDest)
247  dest = MappedDest(actualDestPtr, dest.size());
248  }
249 };
250 
251 namespace internal {
252 template<typename Lhs, typename Rhs, int RhsMode>
253 struct traits<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false> >
254  : traits<ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs> >
255 {};
256 }
257 
258 template<typename Lhs, typename Rhs, int RhsMode>
259 struct SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>
260  : public ProductBase<SelfadjointProductMatrix<Lhs,0,true,Rhs,RhsMode,false>, Lhs, Rhs >
261 {
263 
264  enum {
265  RhsUpLo = RhsMode&(Upper|Lower)
266  };
267 
268  SelfadjointProductMatrix(const Lhs& lhs, const Rhs& rhs) : Base(lhs,rhs) {}
269 
270  template<typename Dest> void scaleAndAddTo(Dest& dest, const Scalar& alpha) const
271  {
272  // let's simply transpose the product
273  Transpose<Dest> destT(dest);
275  Transpose<const Lhs>, 0, true>(m_rhs.transpose(), m_lhs.transpose()).scaleAndAddTo(destT, alpha);
276  }
277 };
278 
279 } // end namespace Eigen
280 
281 #endif // EIGEN_SELFADJOINT_MATRIX_VECTOR_H
#define EIGEN_PRODUCT_PUBLIC_INTERFACE(Derived)
Definition: ProductBase.h:46
const AutoDiffScalar< DerType > & conj(const AutoDiffScalar< DerType > &x)
internal::traits< Derived >::Scalar Scalar
Definition: DenseBase.h:63
#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:104
Expression of the transpose of a matrix.
Definition: Transpose.h:57
#define EIGEN_RESTRICT
iterative scaling algorithm to equilibrate rows and column norms in matrices
Definition: matrix.hpp:471
#define A1
const unsigned int RowMajorBit
void pstore(Scalar *to, const Packet &from)
RealReturnType real() const
static EIGEN_DONT_INLINE void run(Index size, const Scalar *lhs, Index lhsStride, const Scalar *_rhs, Index rhsIncr, Scalar *res, Scalar alpha)
#define EIGEN_LOGICAL_XOR(a, b)
unpacket_traits< Packet >::type predux(const Packet &a)
void rhs(const real_t *x, real_t *f)
#define EIGEN_DONT_INLINE
static Derived::Index first_aligned(const Derived &m)
#define eigen_assert(x)


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Author(s): Milan Vukov, Rien Quirynen
autogenerated on Mon Jun 10 2019 12:35:04